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Search: id:A077538
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| A077538 |
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First differences of triangular numbers with square pyramidal indices. |
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+0
2
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| 1, 14, 90, 360, 1075, 2646, 5684, 11040, 19845, 33550, 53966, 83304, 124215, 179830, 253800, 350336, 474249, 630990, 826690, 1068200, 1363131, 1719894, 2147740, 2656800, 3258125, 3963726, 4786614, 5740840, 6841535, 8104950
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OFFSET
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0,2
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COMMENT
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This sequence is also the sums of a partition of the integers into groups of (n+1)^2 integers starting at 1 and not repeating or skipping any: a(0)=1, a(1)=2+3+4+5=14, a(2)=6+7+8+9+10+11+12+13+14=90, etc.
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FORMULA
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Let SP(m) be the m-th square pyramidal number m*(m+1)*(2*m+1)/6 and let T(k) be the k-th Triangular number k*(k+1)/2; then a(n) = T(SP(n+1))-T(SP(n)) = ((n+1)^2*(n+2)*(2*n^2+2*n+3))/6.
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EXAMPLE
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SP(3)=14, SP(4)=30, T(14)=105 and T(30)=465, so a(3)=465-105=360.
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CROSSREFS
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Sequence in context: A126482 A116343 A034544 this_sequence A114242 A054487 A047639
Adjacent sequences: A077535 A077536 A077537 this_sequence A077539 A077540 A077541
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 09 2002
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EXTENSIONS
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More terms and better description from Bruce Corrigan (scentman(AT)myfamily.com), Nov 14 2002
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